Free vibration analysis of axisymmetric shells with various shapes using Sylvester-transfer stiffness coefficient method

다국어 초록 (Multilingual Abstract)

We developed a computational method for effectively conducting the free vibration analysis of axisymmetric shells with variousshapes. This paper describes a computational algorithm for the free vibration analysis of axisymmetric shells using the Sylvester-transferstiffness coefficient method (S-TSCM). From the free vibration analyses of three axisymmetric shells (joined conical-cylindrical shell,hermetic capsule and built-up shell), we verified the applicability of the S-TSCM. We then confirmed that the computational power ofthe S-TSCM is much better than both the finite element-transfer matrix method and finite element-transfer stiffness coefficient method,in terms of computational accuracy and time. In particular, when axisymmetric shells are modeled into a large number of conical shellelements, the S-TSCM is superior to both the bisection method using Sturm sequence property and Jacobi method, in terms of computationaltime and storage.

참고문헌 (Reference)

1 H. Saunders, "Vibrations of conical shells" 32 (32): 765-772, 1960

2 T. Kondou, "Transfer stiffness coefficient method combined with concept of substructure synthesis method (Linear free and forced vibration analyses of a straight-line beam structure)," 40 (40): 187-196, 1997

3 J. Kang, "Three-dimensional vibration analysis of joined thick conical-cylindrical shells of revolution with variable thickness" 331 : 4187-4198, 2012

4 W. H. Press, "Numerical recipes, the art of scientific computing" Cambridge University Press 447-449, 2007

5 S. K. Sen, "Free vibration of shells of revolution using FEM" 100 (100): 283-303, 1974

6 A. Kalnins, "Free vibration of rotationally symmetric shells" 36 (36): 1355-1365, 1964

7 L. Tong, "Free vibration of orthotropic conical shells" 31 (31): 719-733, 1993

8 T. Irie, "Free vibration of joined conical-cylindrical shells" 95 (95): 31-39, 1984

9 M. A. Kouchakzadeh, "Free vibration analysis of joined cross-ply laminated conical shells" 78 : 118-125, 2014

10 T. Kondou, "Free vibration analysis of a multiple straightline structure regarded as a distributed mass system by the transfer influence coefficient method" 34 (34): 33-41, 1991

11 M. Özakça, "Free vibration analysis and optimization of axisymmetric plates and shells—I. finite element formulation" 52 (52): 1181-1197, 1994

12 최명수, "Free Vibration Analysis of Plate Structures Using Finite Element-Transfer Stiffness Coefficient Method" 대한기계학회 17 (17): 805-815, 2003

13 C. T. F. Ross, "Finite element programs for axisymmetric problems in engineering" Ellis Horwood 105-115, 1984

14 K. J. Bathe, "Finite element procedures" Prentice-Hall 943-945, 1996

15 K. J. Bathe, "Finite element procedures" Prentice-Hall 912-919, 1996

16 E. Efraim, "Exact vibration frequencies of segmented axisymmetric shells" 44 : 281-289, 2006

17 M. S. Tavakoli, "Eigensolutions of joined/hermetic shell structures using the state space method" 100 (100): 97-123, 1989

18 최명수, "Development of free vibration analysis algorithm for beam structures by combining Sylvester’s inertia theorem and transfer stiffness coefficient method" 대한기계학회 26 (26): 11-19, 2012

19 J. W. Demmel, "Applied numerical linear algebra" Siam 202-203, 1997

20 M. A. Dokainish, "A new approach for plate vibration:combination of transfer matrix and finite-element technique" 94 : 526-530, 1972

21 A. Sueoka, "A method of vibrational analysis using a personal computer (A suggested transfer influence coefficient method)," 48 (48): 31-46, 1998